The impact of a teacher education culture-based project on identity as a mathematically thinking teacher

Identity as a mathematics teacher is enhanced when a teacher explores the cultural setting of their mathematics. The reports of projects that link culture and mathematics were analysed to explore the impact of sociocultural situations together with affective and cognitive aspects of self-regulation on identity. The reports were written by pre-service and in-service, mainly secondary, teachers at the University of Goroka, Papua New Guinea. While all 239 reports were read and considered in terms of the thesis of this article, 60 (25%) were analysed in detail developing the argument. The results indicate the strengths of such projects to take account of cultural knowledge when colonised education systems are further modified through reforms that emphasise culture. The significance for teacher education is the role that an activity which links culture and school mathematics plays in building values and identities.     

Learning mathematics and learning to teach: Learning cycles in mathematics teacher education

The reconceptualization of mathematics teacher education based on current mathematics education reform efforts necessitates the elaboration of theoretical frameworks to guide both the practice of and research on teacher education. The author presents a framework which has been useful in shaping two major mathematics teacher education research and development projects. This framework for mathematics teacher learning builds recursively on a framework for mathematics learning which derives from a social constructivist view of learning and incorporates aspects of French didactical theory using the organizing structure of the Karplus Learning Cycle. The framework can be used to think about the content and organization of a particular lesson or of an entire course or program for teachers. Further, it describes the interconnection between different domains of teacher knowledge.     

Language of learning and teaching in schools: an issue for research in mathematics teacher education?

Most countries in Africa have introduced the use of local languages as the language of learning and teaching for the first few years of schooling. Meaning that for the first few years of learning, learners learn mathematics in their local languages. In response to this, most research has focused on the challenges of using local languages in multilingual mathematics classrooms in schools. Not much research focuses on how the teacher educators prepare the prospective teachers to teach mathematics in multilingual classrooms. To further knowledge in the area of multilingualism in mathematics education, I, in this paper, present an analysis of the literature on multilingual teacher education in Africa. Specifically, I look at what it is that governments in interested countries are doing in teacher education programs in response to the introduction of local languages in schools. From the literature examined, I found that although there is awareness in a number of countries of the need for multilingual teacher education, not much has been done in order to train mathematics teachers on how to use local languages in the classroom. I therefore recommend that, for those countries that have implemented or planning to introduce the use of local languages in schools, some reforms should also take place in teacher education programs in terms of training the prospective teachers how to teach in local languages.     

Constructivism: Theory For Practice? The Case Of Mathematics

In recent years the theory known as constructivism has attracted considerable attention from researchers and document writers in particular. Implementation of constructivist principles inside the classroom is still problematic, however. Different reasons for this are explored in the paper. An overview of previously ‐ and in some cases still ‐ popular theories of learning and teaching precedes a detailed discussion of constructivism: its sources, definitions, advocates, and critics. A number of classroom experiments designed and executed within a constructivist paradigm are reported in considerable detail. The roles of both learner and teacher are described. Throughout, the discussion is confined to mathematics, mathematics education, and the mathematics classroom. However, the main arguments presented are applicable as well to other disciplines.     

On Culture and Mathematics Teacher Education

Many countries are multicultural. Mathematics teacher education classes often are composed of students with varied cultural and linguistic backgrounds, and mathematics teachers may be employed in regions from which they do not come. Formal (mathematics) education is a process of cultural interaction, and every child and teacher may experience some degree of social and cultural conflict in that process. This paper describes and reflects on some of these tensions, as they exist in mathematics teacher education in Mozambique. The process of developing among future mathematics teachers an awareness of the social and cultural bases of mathematics is object of reflection.     

Getting the fish out of the water: Considering benefits and problems of doing research on teacher education at an international level

Structure and content of teacher education depend on a deeper rationale, which is a result of cultural boundaries. At the same time teaching is a cultural practice that differs across countries. Like the water in the fish's tank, such cultural givens are too often invisible as we debate research designs. In this article, we focus in particular on the understanding of three main components of teacher education: mathematics, mathematics pedagogy and general pedagogy, and on juxtaposing two extreme models: Germany and the US. It turns out that benefits and problems of international comparisons are closely related to each other.     

HIGHER EDUCATION STATISTICAL INDICATORS FROM FOUR EUROPEAN UNION COUNTRIES ‐ AN OVERVIEW

Statistical indicators can be developed into an appropriate instrument for comparing national education and higher education systems. The present survey, which covers the four European Union countries of Germany, France, the United Kingdom, and the Netherlands, picks up certain of the topics included in the International Education Indicators (INES) project of OECD, and goes on to expand and to examine them in greater depth with special reference to higher education. Quantitative and other data show that the expansion of higher education is typical not only of the Federal Republic of Germany, but also of its western European neighbours. Regulations governing entry into higher education vary substantially among the four countries. Close coordination between school and higher education, rigorous selection procedures, along with intensive monitoring and supervision at the higher education institution explain not only the high success rate of British university students but also ‐ in conjunction with clearly defined curricula ‐ the relatively short period which British students spend there. The higher expenditure on supervision at British and Dutch higher education institutions is reflected in the burden on public finances. However, given the shorter period of study and the higher student success rate in the United Kingdom, one student completing higher education probably costs the British state less than one student completing higher education in Germany.

     

国外中小学数学教育评价研究述评及其启示

数学是基础教育中最为重要的学科之一,世界各国政府和教育部门对数学教育评价都十分重视。美国国家评价管理委员会、国际教育成就评价协会、国际经济合作与发展组织等近年来分别开发了NAEP、TIMSS以及PISA等多个评价项目,对中小学数学教育质量进行系统测查。相关研究中恰当的目标设置、明确的评价范畴以及科学、严格的研究设计等多个方面对我国的数学教育质量评价研究均具有重要的启示和借鉴意义。     

The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five-country analysis using TEDS-M data

This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers’ knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical content knowledge (MPCK) of future teachers in their final year in teacher preparation programs. The purpose of this study is to explore whether elementary teaching candidates’ MCK and MPCK are associated with their opportunities to learn in mathematics courses and mathematics methods courses in five countries. The results showed that opportunities to learn in some teacher preparation components are more important than in other components.     

Discourses about School-based Mathematics Teacher Education in Finland and Sweden

In this cross-case study we focus on school-based teacher education in Sweden and Finland. Through the use of focus-group interviews with mathematics teacher educators in Finland and Sweden, the study shows that there are substantial differences in how school-based teacher education is introduced and portrayed in the discourse about teacher education and prospective teachers' learning. The school-based teacher education among the Finnish groups is made relevant in relation to several aspects of prospective teachers' learning. In the Swedish groups, school-based teacher education is portrayed as an organizational problem and few aspects of prospective teachers' learning are brought into the discourse. The results cannot be generalized to the two countries but show interesting conceptualizations of school-based education potentially useful for teacher educators and scholars.     

美国《中学数学教与学》教材的特点及其对中国数学教师教育的启示

美国《中学数学教与学》是初中年级数学教师教育"数学教学法"课程的教材,其特点表现为:单元主题以数学教学理论为线索呈现,单元内容以具体数学知识为载体展开并且以参与式活动的形式组织教学活动.该教材对我国的数学教师教育有如下启示:数学教师教育课程应以数学知识为载体学习数学教育理论;数学教师教育教材应突出教学方式的示范性,体现做中学,在数学教学活动中学习数学教学方法;数学教师教育应注重教师学科专业素质的提升.     

Future Directions in Research on Mathematics-Related Teacher Identity

Mathematics education research has placed great emphasis on teacher identity, examining both pre- and in-service teachers, and within these cohorts, specialised mathematics teachers and non-specialists such as elementary teachers. Extensive research has already been done; hence, this paper discusses possible future directions for research on teacher identity in mathematics education. Among other issues, we highlight that general education research on identity has infrequently informed research on mathematics-related teacher identity. This not only limits the transfer of knowledge but also isolates mathematics education from general education research. We suggest that connecting these lines of research and their findings may not only strengthen mathematics education research and mathematics teaching and learning but also contribute to less isolation within the discipline as a whole.     

The Assessment of Mathematics and Science Teacher Quality

The purpose of this study was to examine the types of instruments being used to document mathematics and science teacher quality characteristics in 48 nationally funded mathematics and science education awards. Each of the 48 projects operationalized teacher quality and determined how to assess it. The main research questions examined the instruments awardees used to gather data on mathematics and science teacher quality, and the main characteristics of teachers examined by awardees. Results showed that awardees most frequently used surveys or questionnaires to assess characteristics of mathematics and science teacher quality. The most common teacher characteristics examined by awardees' included teacher behaviors, practices, and beliefs, followed by the assessment of subject and pedagogical knowledge, and the documentation of mathematics and science teachers' certification. A few new instruments were under development and in use to assess characteristics of teacher quality. Detailed information on the development and psychometric properties of the instruments used for these examinations was not available from the reports. Because awardees were at different stages in their funded activities and data collection efforts were ongoing at the time of this analysis, this study offers a preliminary and formative review of the use of assessments to document mathematics and science teacher quality characteristics among these awards.     

Comparative study of teaching content in teacher education programmes in Canada,Denmark, Finland and Singapore

This article presents the results of a comparative study of the content in selected teacher education programmes for primary and lower secondary teachers in Canada, Denmark, Finland and Singapore. First and foremost, the study is a comparison between teacher education programmes in, on the one hand, Canada, Finland and Singapore, all of which score highly in international comparisons such as PISA and TIMMS, and on the other hand Denmark, which receives average scores, but it also functions as a comparison between all four countries. The study covers the following subjects: pedagogy and mathematics. The study does not offer proof of any clear difference between the Danish teacher education programmes and those found in the top-performing countries. Two main findings are: (1) philosophically based professional knowledge, much of which is normative in character, forms an extensive part of the body of professional knowledge within the Danish teacher education programmes, which is not true of the programmes in the Top-3 countries and (2) the programmes in Canada and Singapore more frequently employ literature combining research-based knowledge with practical guidance and experiences, while the programmes in Denmark and Finland keep these knowledge forms separate.     

Assessment for learning in Norway and Portugal: the case of primary school mathematics teaching

In this study, we aim to understand the forces driving assessment for learning (AfL) in primary school teaching. By applying a case study design, including the two cases of Norway and Portugal and using mathematics teaching as an example, available policy documents and research reports are analysed to identify the differences and similarities that might explain the assessment practices previously observed in the two countries. Many similarities are found at the school and national levels. In particular, AfL is introduced as a national policy in both countries. Still, AfL practices are not common in primary mathematics classrooms in either country, although this is true for different reasons in each country. It is suggested that the assessment culture caused by national policies, such as curriculum reforms, national professional development projects and teacher autonomy, explains the similarities in the observed outcomes.     

Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs are a good place to start the process of redesigning mathematics curricula so that school mathematics will pay more than lip service to problem posing. Data are presented and analyzed showing that teacher education students can recognize the need for problem posing both in their own programs and in school mathematics curricula. Examples of problems posed by teacher education students are presented and discussed. An active learning framework for interpreting the role of problem posing in mathematics classrooms is presented.     

Establishing mathematics for teaching within classroom interactions in teacher education

Teacher educators’ processes of establishing “mathematics for teaching” in teacher education programs have been recognized as an important area for further research. In this study, we examine how two teacher educators establish and make explicit features of mathematics for teaching within classroom interactions. The study shows how the establishment of mathematics for teaching is dependent on the use of keywords from the mathematics education domain, the introduction of variation, and the use of generic communicative strategies. As such, the study could be seen as a contribution to ongoing research on how mathematics teacher educators interactively deal with mathematics for teaching.     

韩国职前数学教师教育的评介与分析

韩国的数学教师职前教育体制有如下特点:类型多样的教师职前培养机构、严格的公立学校数学教师聘任制度、定期的教师教育机构评估制度.小学数学教师教育课程具有综合性、多样化特点;中学数学教师教育课程更重视学科知识.韩国数学教师职前教育对中国的数学教师教育有如下启示:建立多元的办学体制,致力于专业化的数学教师培养;以教师聘任制度和教师教育机构评估制度促进数学教师培养质量的提高;在学科课程和教学法课程之间寻求恰当平衡.     

中美职前小学教师教育中数学课程的比较研究——以上海师范大学和纽约城市大学为例

教师教育中数学知识的获得是影响职前小学教师数学知识的主要因素之一,以我国上海师范大学和美国纽约城市大学小学教育专业本科培养的数学课程计划为个案,从数学内容类课程和数学方法类课程两方面研究发现,两国职前小学教师教育中各数学课程在学分要求、教学目标、教学内容和教学方法等方面存在差异。美国职前小学教师本科培养的经验,对我国职前小学教育专业本科培养的数学课程设置与实施应该如何加强联系小学数学课程与教学实际具有一定借鉴。     

The CERI INSET project: a description and a preliminary evaluation of international co‐development work

Between 1975 and 1980 the Organization for European Co‐operation and Development's (OECD) Centre for Educational Research and Innovation (CERI) engaged in a major project to enable its member countries to share experience of innovatory approaches to the in‐service education of teachers. This paper refers briefly to one strand of the project ‐ the collection and synthesis of case‐study material ‐ and describes in more detail the second strand: the co‐development work on the themes of teacher participation, evaluation, training the trainers, and the development of training materials. A preliminary evaluation is offered of the benefits gained in terms of accessing the international network, the motivation of participants, the development of in‐service education for teachers (INSET) research, and influences on national policy.